Hybrid physics-based and machine learning models for reservoir simulations

Abstract

System and methods for simulating fluid flow during downhole operations are provided. Measurements of an operating variable at one or more locations within a formation are obtained from a downhole tool disposed in a wellbore within the formation during a current stage of a downhole operation being performed along the wellbore. The obtained measurements are applied as inputs to a hybrid model of the formation. The hybrid model includes physics-based and machine learning models that are coupled together within a simulation grid. Fluid flow within the formation is simulated, based on the inputs applied to the hybrid model. A response of the operating variable is estimated for a subsequent stage of the downhole operation along the wellbore, based on the simulation. Flow control parameters for the subsequent stage are determined based on the estimated response. The subsequent stage of the operation is performed according to the determined flow control parameters.

What is claimed is: 
     
       1. A computer-implemented method of simulating fluid flow during downhole operations, the method comprising:
 obtaining, by a computer system from a downhole tool disposed in a wellbore within a formation, measurements of an operating variable at one or more locations within the formation during a current stage of a downhole operation being performed along the wellbore; 
 applying the obtained measurements as inputs to a hybrid model of the formation, the hybrid model including physics-based and machine learning models that are coupled together within a simulation grid; 
 simulating fluid flow within the formation, based on the inputs applied to the hybrid model; 
 estimating a response of the operating variable for a subsequent stage of the downhole operation to be performed along the wellbore, based on the simulation; 
 determining flow control parameters for the subsequent stage of the downhole operation to be performed, based on the estimated response; and 
 performing the subsequent stage of the downhole operation according to the determined flow control parameters. 
 
     
     
       2. The method of  claim 1 , further comprising:
 monitoring an actual response of the operating variable, based on additional measurements obtained from the downhole tool as the subsequent stage of the downhole operation is performed along the wellbore; and 
 upon determining that a difference between the actual response and the estimated response exceeds an error tolerance threshold, updating the hybrid model based on the difference. 
 
     
     
       3. The method of  claim 1 , wherein the downhole operation is a stimulation treatment, and applying the obtained measurements comprises:
 determining whether the one or more locations at which the measurements were obtained correspond to a fracture within the formation; 
 when it is determined that the one or more locations correspond to a fracture within the formation:
 designating one or more of a plurality of cells corresponding to the one or more locations within the simulation grid as a fractured region of the hybrid model; and 
 assigning at least one of a physics-based model or a machine learning model to the fractured region within the simulation grid; and 
 
 when it is determined that the one or more locations do not correspond to a fracture within the formation, designating one or more of the plurality of cells corresponding to the one or more locations within the simulation grid as a non-fractured region of the hybrid model. 
 
     
     
       4. The method of  claim 3 , wherein the physics-based model is at least one of a finite difference (FD) model or a smoothed particle hydrodynamics (SPH) model. 
     
     
       5. The method of  claim 3 , wherein the machine learning model is a neural network. 
     
     
       6. The method of  claim 5 , wherein the neural network is at least one of a recurrent deep neural network (DNN) or a long short-term memory (LSTM) deep neural network. 
     
     
       7. The method of  claim 5 , wherein applying the obtained measurements to the hybrid model comprises:
 training the neural network to estimate the response of the one or more operating variables to fluid injection, based on a portion of the measurements obtained during the current stage of the stimulation treatment and a cost function associated with each of the one or more operating variables; 
 determining an actual response of the one or more operating variables, based on additional measurements obtained during the subsequent stage of the stimulation treatment along the wellbore; 
 determining whether a difference between the actual response and the estimated response exceeds an error tolerance threshold; and 
 when the difference is determined to exceed the error tolerance threshold, retraining the neural network using the additional measurements. 
 
     
     
       8. The method of  claim 7 , wherein the retraining comprises:
 applying Bayesian optimization to retrain the neural network over a plurality of iterations until a predetermined convergence criterion is met. 
 
     
     
       9. The method of  claim 7 , further comprising:
 determining boundary conditions for an interface between the fractured and non-fractured regions of the hybrid model, 
 wherein the fluid flow is simulated for the subsequent stage of the downhole operation, based on the determined boundary conditions. 
 
     
     
       10. A system comprising:
 a processor; and 
 a memory coupled to the processor, the memory having instructions stored therein, which, when executed by the processor, cause the processor to perform a plurality of functions, including functions to: 
 obtain, from a downhole tool disposed in a wellbore within a formation, measurements of an operating variable at one or more locations within the formation during a current stage of a downhole operation being performed along the wellbore; 
 apply the obtained measurements as inputs to a hybrid model of the formation, the hybrid model including physics-based and machine learning models that are coupled together within a simulation grid; 
 simulate fluid flow within the formation, based on the inputs applied to the hybrid model; 
 estimate a response of the operating variable for a subsequent stage of the downhole operation to be performed along the wellbore, based on the simulation; 
 determine flow control parameters for the subsequent stage of the downhole operation to be performed, based on the estimated response; and 
 perform the subsequent stage of the downhole operation according to the determined flow control parameters. 
 
     
     
       11. The system of  claim 10 , wherein the functions performed by the processor further include functions to:
 monitor an actual response of the operating variable, based on additional measurements obtained from the downhole tool as the subsequent stage of the downhole operation is performed along the well bore; 
 determine whether a difference between the actual response and the estimated response exceeds an error tolerance threshold; and 
 when a difference between the actual response and the estimated response is determined to exceed the error tolerance threshold, update the hybrid model based on the difference. 
 
     
     
       12. The system of  claim 10 , wherein the downhole operation is a stimulation treatment, and the functions performed by the processor further include functions to:
 determine whether the one or more locations at which the measurements were obtained correspond to a fracture within the formation; 
 when it is determined that the one or more locations correspond to a fracture within the formation:
 designate one or more of a plurality of cells corresponding to the one or more locations within the simulation grid as a fractured region of the hybrid model; and 
 assign at least one of a physics-based model or a machine learning model to the fractured region within the simulation grid; and 
 
 when it is determined that the one or more locations do not correspond to a fracture within the formation, designate one or more of the plurality of cells corresponding to the one or more locations within the simulation grid as a non-fractured region of the hybrid model. 
 
     
     
       13. The system of  claim 12 , wherein the physics-based model is at least one of a finite difference (FD) model or a smoothed particle hydrodynamics (SPH) model. 
     
     
       14. The system of  claim 12 , wherein the machine learning model is a neural network. 
     
     
       15. The system of  claim 14 , wherein the neural network is at least one of a recurrent deep neural network (DNN) or a long short-term memory (LSTM) deep neural network. 
     
     
       16. The system of  claim 14 , wherein the functions performed by the processor further include functions to:
 train the neural network to estimate the response of the one or more operating variables to fluid injection, based on a portion of the measurements obtained during the current stage of the stimulation treatment and a cost function associated with each of the one or more operating variables; 
 determine an actual response of the one or more operating variables, based on additional measurements obtained during the subsequent stage of the stimulation treatment along the wellbore; 
 determine whether a difference between the actual response and the estimated response exceeds an error tolerance threshold; and 
 when the difference is determined to exceed the error tolerance threshold, retrain the neural network using the additional measurements. 
 
     
     
       17. The system of  claim 16 , wherein the functions performed by the processor further include functions to:
 apply Bayesian optimization to retrain the neural network over a plurality of iterations until a predetermined convergence criterion is met. 
 
     
     
       18. The system of  claim 16 , wherein the functions performed by the processor further include functions to:
 determine boundary conditions for an interface between the fractured and non-fractured regions of the hybrid model, 
 wherein the fluid flow is simulated for the subsequent stage of the downhole operation, based on the determined boundary conditions. 
 
     
     
       19. A non-transitory computer-readable storage medium having instructions stored therein, which, when executed by a computer, cause the computer to perform a plurality of functions, including functions to:
 obtain, from a downhole tool disposed in a wellbore within a formation, measurements of an operating variable at one or more locations within the formation during a current stage of a downhole operation being performed along the wellbore; 
 apply the obtained measurements as inputs to a hybrid model of the formation, the hybrid model including physics-based and machine learning models that are coupled together within a simulation grid; 
 simulate fluid flow within the formation, based on the inputs applied to the hybrid model; 
 estimate a response of the operating variable for a subsequent stage of the downhole operation to be performed along the wellbore, based on the simulation; 
 determine flow control parameters for the subsequent stage of the downhole operation to be performed, based on the estimated response; and 
 perform the subsequent stage of the downhole operation according to the determined flow control parameters. 
 
     
     
       20. The non-transitory computer-readable storage medium of  claim 19 , wherein the functions performed by the computer further include functions to:
 monitor an actual response of the operating variable, based on additional measurements obtained from the downhole tool as the subsequent stage of the downhole operation is performed along the wellbore; 
 determine whether a difference between the actual response and the estimated response exceeds an error tolerance threshold; and 
 when a difference between the actual response and the estimated response is determined to exceed the error tolerance threshold, update the hybrid model based on the difference.